Unsupervised non-parametric region segmentation using level sets

We present a novel non-parametric unsupervised segmentation algorithm based on region competition (Zhu and Yuille, 1996); but implemented within a level sets framework (Osher and Sethian, 1988). The key novelty of the algorithm is that it can solve N ≥ 2 class segmentation problems using just one embedded surface; this is achieved by controlling the merging and splitting behaviour of the level sets according to a minimum description length (MDL) (Leclerc (1989) and Rissanen (1985)) cost function. This is in contrast to N class region-based level set segmentation methods to date which operate by evolving multiple coupled embedded surfaces in parallel (Chan et al., 2002). Furthermore, it operates in an unsupervised manner; it is necessary neither to specify the value of N nor the class models a-priori. We argue that the level sets methodology provides a more convenient framework for the implementation of the region competition algorithm, which is conventionally implemented using region membership arrays due to the lack of a intrinsic curve representation. Finally, we generalise the Gaussian region model used in standard region competition to the non-parametric case. The region boundary motion and merge equations become simple expressions containing cross-entropy and entropy terms.